$\backslash$table$[[$Region$,$T$,$F$,$Total$],[$S$,67,54,121],[$U$,70,59,129],[$Total$,137,113,],[,,,],[$Mar$.$St$.,$T$,$F$,$Total$],[$M$,13$

$\backslash$table$[[$Region$,$T$,$F$,$Total$],[$S$,67,54,121],[$U$,70,59,129],[$Total$,137,113,],[,,,],[$Mar$.$St$.,$T$,$F$,$Total$],[$M$,133,66,199],[$S$,4,47,51],[$Total$,137,113,],[$Income$,$T$,$F$,$Total$],[$L$,5,53,58],[$M$,63,24,87],[$H$,69,36,105],[$Total$,137,113,],[,,,],[$M$,,,],[$M$,,,],[$M$,,,]]3,66,199],[$S$,4,47,51],[$Total$,137,113,],[$Income$,$T$,$F$,$Total$],[$L$,5,53,58],[$M$,63,24,87],[$H$,69,36,105],[$Total$,137,113,],[,,,],[$M$,,,],[$M$,,,],[$M$,,,]]$

There are three attributes to consider when predicting whether purchase is true or false:

Region: Suburban or Urban

Marital Status: Married or Single

Income: High, Medium, or Low

Answer the following questions:

a$.$ What is the best single$-$attribute decision rule and what is its associated error?

b$.$ What is the information measure of the entire data set?

c$.$ What is the information gain for splitting on Region? Marital Status? Income? Based on this, pick the initial attribute to split on$.$

d$.$ Complete one more level of the decision tree and stop $($i$.$e$.,$ each leaf tests no more than $2$ attributes$).$